Remark 3.7 The same weighted Laplacian matrix has been studied in [1]}, as well as a symmetric version in [2]}, [3]}. The Laplace operator \(L_{(G,\upsilon ,\varepsilon )}\)  coincides with the Laplacian studied by Friedman and Tillich [4]}, who also considered graphs with general vertex and edge measures, and the operator of Horak and Jost [5]}, who defined a Laplacian for weighted simplicial complexes, for graphs.

